Stahl repeatedly challenged the education secretary, at one point suggesting that DeVos should visit underperforming public schools to learn about their problems. DeVos responded, “Maybe I should.” The secretary also said she is “not so sure exactly” how she became, as Stahl described her, “the most hated” member of President Trump’s Cabinet but believes that she is “misunderstood.”

These are just some of the things that DeVos said — or couldn’t answer — during the interview:

She couldn’t say whether the number of false accusations of sexual assault on school campuses is lower than the number of actual rapes or assaults.

Arming teachers “should be an option” for states and communities, she said, even though she couldn’t “ever imagine” her first-grade teacher, Mrs. Zorhoff, having had a gun.

“We have invested billions and billions and billions of dollars from the federal level, and we have seen zero results,” DeVos said — a statement Stahl challenged.

“I hesitate to talk about all schools in general because schools are made up of individual students attending them.”

In reference to the #MeToo movement, she said she experienced moments decades ago that “today would just be viewed as unacceptable.”

DeVos, who rarely gives interviews to journalists, is a longtime school choice advocate who once said that traditional public education is “a dead end,” and she has made clear that her top priority as the nation’s education chief is expanding alternatives to traditional public schools. She is a champion of using public funds for private and religious school education, and critics say she is determined to privatize public education. DeVos has denied that.

DeVos, a billionaire who has spent millions of dollars on school efforts in her home state of Michigan, has been perhaps the most controversial of Trump’s Cabinet members. She became the first Cabinet nominee in history to need a tie-breaking vote from the vice president to be confirmed by the Senate. Her January 2017 confirmation hearing before the Senate education panel was marked by her inability to answer basic questions about education.

In the “60 Minutes” interview, more than a year after becoming education secretary, DeVos again had trouble answering questions and seemed to contradict herself. For example, she and Stahl had this conversation about what happens to underperforming traditional public schools when children leave for alternatives and take funding with them:

STAHL: Why take away money from that school that’s not working — to bring them up to a level where they are, that school is working?

DEVOS: Well, we should be funding and investing in students, not in school, school buildings, not in institutions, not in systems.

STAHL: Okay. But what about the kids who are back at the school that’s not working? What about those kids?

DEVOS: Well, in places where there have been, where there is, a lot of choice that’s been introduced, Florida, for example, the studies show that when there’s a large number of students that opt to go to a different school or different schools, the traditional public schools actually, the results get better, as well.

STAHL: Now, has that happened in Michigan? We’re in Michigan. This is your home state.

DEVOS: Yes, well, there’s lots of great options and choices for students here.

STAHL: Have the public schools in Michigan gotten better?

DEVOS: I don’t know. Overall, I, I can’t say overall that they have all gotten better.

STAHL: The whole state is not doing well.

DEVOS: Well, there are certainly lots of pockets where this, the students are doing well and …

STAHL: No, but your argument that if you take funds away that the schools will get better is not working in Michigan, where you had a huge impact and influence over the direction of the school system here.

DEVOS: I hesitate to talk about all schools in general because schools are made up of individual students attending them.

STAHL: The public schools here are doing worse than they did.

DEVOS: Michigan schools need to do better. There is no doubt about it.

STAHL: Have you seen the really bad schools? Maybe try to figure out what they’re doing?

DEVOS: I have not, I have not, I have not intentionally visited schools that are underperforming.

STAHL: Maybe you should.

DEVOS: Maybe I should. Yes.

And there was this exchange about DeVos and her popularity — or, rather, lack of it:

STAHL: Why have you become, people say, the most hated Cabinet secretary?

DEVOS: I’m not so sure exactly how that happened. But I think there are a lot of really powerful forces allied against change.

STAHL: Does it hurt?

DEVOS: Sometimes it does. Sometimes it does. Again, I think, I think …

STAHL: Do you ever say …

DEVOS: I’m more misunderstood than anything.

Stahl asked DeVos about her decision last year to rescind Obama-era Title IX guidelines on how schools should handle sexual assault allegations. DeVos, saying that too many men were falsely accused, set new rules making it harder for accusers to prove their accusations.